If u r starting from Lahore at night then next day do not stop at Abbottabad and carry on for Chilas. I have done it twice. Took 12 a.m. buses from Lahore to Mansehra then got jeep and reached Chilas around 7-8 p.m. There are no security issues while travelling in Abbottabad Mansehra area.
Just take rain coats and hiking sticks with u and joggers with good grip will do the job as it is gravel, soil trek and no glacier crossings till Beyal Camp and the width is normally reasonable. Most of the trek has trees around the trek.
Your idea is good. One day visit to NP base camp is only recommended for experienced trekkers as weather can go bad any moment. Yes, u can view whole landscape of Nanga Parbat even from Fairy Meadows and also from the area ahead of Beyal Camp. You can return back once u get a good view provided cloud cover allows u to gaze at Nanga Parbat 
Get up early morning, offer Fajr prayers and enjoy early morning views of Nanga Parbat. Early morning rays at the peaks are amazing 
Then leave by max 6-6: 30 a.m. and reach Raikot bridge around 9: 30 - 10. Then u should be able to make it in time In Sha Allah till Jalkhad.
Huts are there in Beyal Camp but take camps from Fairy Meadows if u do not have your own equipment. The rent should be nominal around 200-300 or so.
Answered above.
You will need around 8-10 hours to reach Besham from Raikot bridge. So, u cannot cross Shangla on same day. Road is good but there is no point crossing Shangla in the dark as u wont be able to see anything. Stay at Besham as there are lots of hotels there. Then next morning cross Shangla and then continue the route to Mingora and onwards to Mardan. But one important thing is that the moment u will go down from Shangla u will face very hot weather while Babusar and Kaghan side weather will be pleasant till Balakot.
Drop idea to visit Kalam as it would be 2 days detour at minimum.